Abstract：Iron-based superconductors and topological matters have been two important research frontiers in condensed matter physics. Here we discuss the recent progress to bridge these two fields. It has been found that iron_x0002_based superconductors can be considered as connate topological superconductors in which there are topological nontrivial bands, coexisting with bands that are responsible for superconductivity. We review several different
cases that nontrivial topological physics arises in iron-based superconductors. In particular, we will address two recent theoretical progresses, the rich topological vortex states in these materials, and a high order topological superconductivity state defined by s± pairing symmetry. The flexible realizations of the topology physics make iron-based superconductors to be unique topological materials and provide opportunities to realize topological superconductivity and Majorana modes at high temperature.